Automatic grouping using smooth-threshold estimating equations

Ueki, Masao; Kawasaki, Yoshinori

doi:10.1214/11-ejs608

Cited by 7 publications

(9 citation statements)

References 24 publications

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“…Note that for each covariate, the total number of constraints is

s = K + C false(K, 2 false)

. Ueki () and Ueki and Kawasaki () considered a similar problem of variable grouping in a much simpler setting of single cross‐sectional study (i.e.,

K = 1

m = 1

), where the

ℓ_{2}

‐norm penalty for group lasso was used. Equivalently, we may write the above fused lasso penalty

P false(β false)

in a matrix notation:

P false(β false) = ∥ D β ∥_{1} = ∥ W B β ∥_{1}

, where

∥ \cdot ∥_{1}

L_{1}

‐norm on

R^{sp}

boldB

is an

italicsp \times italicKp

matrix that defines sp constraints involving p covariates across K studies, and

boldW

is an

italicsp \times italicsp

diagonal matrix containing all weights corresponding to the constraints in

boldB

.…”

Section: Formulation and Methodsmentioning

confidence: 99%

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Fused Lasso with the Adaptation of Parameter Ordering in Combining Multiple Studies with Repeated Measurements

Wang

Song

2016

Biometrics

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Summary Combining multiple studies is frequently undertaken in biomedical research to increase sample sizes for statistical power improvement. We consider the marginal model for the regression analysis of repeated measurements collected in several similar studies with potentially different variances and correlation structures. It is of great importance to examine whether there exist common parameters across study-specific marginal models so that simpler models, sensible interpretations and meaningful efficiency gain can be obtained. Combining multiple studies via the classical means of hypothesis testing involves a large number of simultaneous tests for all possible subsets of common regression parameters, in which it results in unduly large degrees of freedom and low statistical power. We develop a new method of fused lasso with the adaptation of parameter ordering (FLAPO) to scrutinize only adjacent-pair parameter differences, leading to a substantial reduction for the number of involved constraints. Our method enjoys the oracle properties as does the full fused lasso based on all pairwise parameter differences. We show that FLAPO gives estimators with smaller error bounds and better finite sample performance than the full fused lasso. We also establish a regularized inference procedure based on bias-corrected FLAPO. We illustrate our method through both simulation studies and an analysis of HIV surveillance data collected over five geographic regions in China, in which the presence or absence of common covariate effects are reflective to relative effectiveness of regional policies on HIV control and prevention.

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“…Note that for each covariate, the total number of constraints is

s = K + C false(K, 2 false)

. Ueki () and Ueki and Kawasaki () considered a similar problem of variable grouping in a much simpler setting of single cross‐sectional study (i.e.,

K = 1

m = 1

), where the

ℓ_{2}

‐norm penalty for group lasso was used. Equivalently, we may write the above fused lasso penalty

P false(β false)

in a matrix notation:

P false(β false) = ∥ D β ∥_{1} = ∥ W B β ∥_{1}

, where

∥ \cdot ∥_{1}

L_{1}

‐norm on

R^{sp}

boldB

is an

italicsp \times italicKp

matrix that defines sp constraints involving p covariates across K studies, and

boldW

is an

italicsp \times italicsp

diagonal matrix containing all weights corresponding to the constraints in

boldB

.…”

Section: Formulation and Methodsmentioning

confidence: 99%

“…Note that for each covariate, the total number of constraints is s = K + C(K, 2). Ueki (2009) and Ueki and Kawasaki (2011) considered a similar problem of variable grouping in a much simpler setting of single cross-sectional study (i.e., K = 1, m = 1), where the 2 -norm penalty for group lasso was used.…”

Section: Formulation and Methodsmentioning

confidence: 99%

Fused Lasso with the Adaptation of Parameter Ordering in Combining Multiple Studies with Repeated Measurements

Wang

Song

2016

Biometrics

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“…For this step, we employ the smooth-thresholding developed by one of us [53,54] that applies to the ridge logistic regression method, termed the ridge smooth-thresholding logistic regression. We explain the procedure in detail in what follows.…”

Section: Methodsmentioning

confidence: 99%

Ultrahigh-dimensional variable selection method for whole-genome gene-gene interaction analysis

Ueki

Tamiya

2012

BMC Bioinformatics

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BackgroundGenome-wide gene-gene interaction analysis using single nucleotide polymorphisms (SNPs) is an attractive way for identification of genetic components that confers susceptibility of human complex diseases. Individual hypothesis testing for SNP-SNP pairs as in common genome-wide association study (GWAS) however involves difficulty in setting overall p-value due to complicated correlation structure, namely, the multiple testing problem that causes unacceptable false negative results. A large number of SNP-SNP pairs than sample size, so-called the large p small n problem, precludes simultaneous analysis using multiple regression. The method that overcomes above issues is thus needed.ResultsWe adopt an up-to-date method for ultrahigh-dimensional variable selection termed the sure independence screening (SIS) for appropriate handling of numerous number of SNP-SNP interactions by including them as predictor variables in logistic regression. We propose ranking strategy using promising dummy coding methods and following variable selection procedure in the SIS method suitably modified for gene-gene interaction analysis. We also implemented the procedures in a software program, EPISIS, using the cost-effective GPGPU (General-purpose computing on graphics processing units) technology. EPISIS can complete exhaustive search for SNP-SNP interactions in standard GWAS dataset within several hours. The proposed method works successfully in simulation experiments and in application to real WTCCC (Wellcome Trust Case–control Consortium) data.ConclusionsBased on the machine-learning principle, the proposed method gives powerful and flexible genome-wide search for various patterns of gene-gene interaction.

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“…We examine applicability of existing sparse regression for prediction of bank telemarketing success. In particular, we consider the lasso, smoothlyclipped absolute deviation (SCAD, Fan and Li, 2001), minimum concave penalty (MCP, Zhang, 2010) and the smooth-threshold estimating equations (STEE, Ueki, 2009;Ueki and Kawasaki, 2011). Most of the popular sparse regression methods attempt to set irrelevant regression coefficients of predictor variables as zero.…”

Section: Introductionmentioning

confidence: 99%

“…Most of the popular sparse regression methods attempt to set irrelevant regression coefficients of predictor variables as zero. On the other hand, the method by Ueki and Kawasaki (2011) aims at automatic grouping which is an alternative to sparse modeling for variable selection. Automatic grouping gathers similar regression coefficients into a single one.…”

Section: Introductionmentioning

confidence: 99%

Sparse Predictive Modeling for Bank Telemarketing Success Using Smooth-Threshold Estimating Equations

Kawasaki

Ueki

2015

Journal of the Japanese Society of Computational Statistics

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In this paper, we attempt to build and evaluate several predictive models to predict success of telemarketing calls for selling bank long-term deposits using a publicly available set of data from a Portuguese retail bank collected from 2008 to 2013 (Moro et al., 2014, Decision Support Systems). The data include multiple predictor variables, either numeric or categorical, related with bank client, product and social-economic attributes. Dealing with a categorical predictor variable as multiple dummy variables increases model dimensionality, and redundancy in model parameterization must be of practical concern. This motivates us to assess prediction performance with more parsimonious modeling. We apply contemporary variable selection methods with penalization including lasso, elastic net, smoothly-clipped absolute deviation, minimum concave penalty as well as the smooth-threshold estimating equation. In addition to variable selection, the smooth-threshold estimating equation can achieve automatic grouping of predictor variables, which is an alternative sparse modeling to perform variable selection and could be suited to a certain problem, e.g., dummy variables created from categorical predictor variables. Predictive power of each modeling approach is assessed by repeating cross-validation experiments or sample splitting, one for training and another for testing.

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Automatic grouping using smooth-threshold estimating equations

Cited by 7 publications

References 24 publications

Fused Lasso with the Adaptation of Parameter Ordering in Combining Multiple Studies with Repeated Measurements

Fused Lasso with the Adaptation of Parameter Ordering in Combining Multiple Studies with Repeated Measurements

Ultrahigh-dimensional variable selection method for whole-genome gene-gene interaction analysis

Sparse Predictive Modeling for Bank Telemarketing Success Using Smooth-Threshold Estimating Equations

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